Channel Assignment Method Using Parallel Tabu Search Based on Graph Theory in Wireless Sensor Networks

Wireless sensor networks are suffering from serious frequency interference.In this paper,we propose a channel assignment algorithm based on graph theory in wireless sensor networks.We first model the conflict infection graph for channel assignment with the goal of global optimization minimizing the total interferences in wireless sensor networks.The channel assignment problem is equivalent to the generalized graph-coloring problem which is a NP-complete problem.We further present a meta-heuristic Wireless Sensor Network Parallel Tabu Search(WSN-PTS) algorithm,which can optimize global networks with small numbers of iterations.The results from a simulation experiment reveal that the novel algorithm can effectively solve the channel assignment problem.

ACS-based resource assignment and task scheduling in grid

To solve the deadlock problem of tasks that the interdependence between tasks fails to consider during the course of resource assignment and task scheduling based on the heuristics algorithm, an improved ant colony system （ACS） based algorithm is proposed. First, how to map the resource assignment and task scheduling （RATS） problem into the optimization selection problem of task resource assignment graph （TRAG） and to add the semaphore mechanism in the optimal TRAG to solve deadlocks are explained. Secondly, how to utilize the grid pheromone system model to realize the algorithm based on ACS is explicated. This refers to the construction of TRAG by the random selection of appropriate resources for each task by the user agent and the optimization of TRAG through the positive feedback and distributed parallel computing mechanism of the ACS. Simulation results show that the proposed algorithm is effective and efficient in solving the deadlock problem.

Dependent task assignment algorithm based on particle swarm optimization and simulated annealing in ad-hoc mobile cloud

In order to solve the problem of efficiently assigning tasks in an ad-hoc mobile cloud( AMC),a task assignment algorithm based on the heuristic algorithm is proposed. The proposed task assignment algorithm based on particle swarm optimization and simulated annealing( PSO-SA) transforms the dependencies between tasks into a directed acyclic graph( DAG) model. The number in each node represents the computation workload of each task and the number on each edge represents the workload produced by the transmission. In order to simulate the environment of task assignment in AMC,mathematical models are developed to describe the dependencies between tasks and the costs of each task are defined. PSO-SA is used to make the decision for task assignment and for minimizing the cost of all devices,which includes the energy consumption and time delay of all devices.PSO-SA also takes the advantage of both particle swarm optimization and simulated annealing by selecting an optimal solution with a certain probability to avoid falling into local optimal solution and to guarantee the convergence speed. The simulation results show that compared with other existing algorithms,the PSO-SA has a smaller cost and the result of PSO-SA can be very close to the optimal solution.

Frequency Assignment through Combinatorial Optimization Approach

An L（2, 1）-labeling of a graph G is a function f from the vertex set V（G） to the set of all nonnegative integers such that ｜f（x） - f（y）｜ 〉 2 if d（x, y） = 1 and ｜f（x）-f（y）｜ ≥ 1 ifd（x, y） = 2. The L（2, 1）-labeling number λ（G） of G is the smallest number k such that G has an L（2, 1）-labeling with max{f（v） ： v ∈ V（G）} = k. We study the L（3, 2, 1）-labeling which is a generalization of the L（2, 1）-labeling on the graph formed by the （Cartesian） product and composition of 3 graphs and derive the upper bounds of λ3（G） of the graph.

Radio channel assignment

Discusses how to assign a set of noninterference radio channels to a symmetric network of transmitter location over a large planar area, the minimum of the span and the assignment of the channels with the changing of minimum distance among the same channels and the changing of the minimum difference among the adjacent channels. The minimum interval in the frequency spectrum of 9 interger channels is proved and obtained by using the graphic theory and the reduction to absurdity on condition that interference from nearby transmitters is avoided in the whole given grid and the grid spreading arbitrarily far in all directions.

Application of k-person and k-task maximal efficiency assignment algorithm to water piping repair

Solving the absent assignment problem of the shortest time limit in a weighted bipartite graph with the minimal weighted k-matching algorithm is unsuitable for situations in which large numbers of problems need to be addressed by large numbers of parties. This paper simplifies the algorithm of searching for the even alternating path that contains a maximal element using the minimal weighted k-matching theorem and intercept graph. A program for solving the maximal efficiency assignment problem was compiled. As a case study, the program was used to solve the assignment problem of water piping repair in the case of a large number of companies and broken pipes, and the validity of the program was verified.

Independent Cycle Time Assignment for Min-max Systems

A variety of problems in digital circuits, computer networks, automated manufacturing plants, etc., can be modeled as min-max systems. The cycle time is an important performance metric of such systems. In this paper, we focus on the cycle time assignment of minimax systems which corresponds to the pole assignment problem in traditional linear control systems. For the min- max system with max-plus inputs and outputs, we show that the cycle time can be assigned disjointedly by a state feedback, if and only if the system is reachable. Furthermore, a necessary and sufficient condition for the cycle time to be assigned independently by a state feedback is given. The methods are constructive, and some numerical examples are given to illustrate how the methods work in practice.

L(2,1)-labeling problem on distance graphs

L (2, 1)-labeling number, λ(G( Z , D)) , of distance graph G( Z , D) is studied. For general finite distance set D , it is shown that 2D+2≤λ(G( Z , D))≤D 2+3D. Furthermore, λ(G( Z , D)) ≤8 when D consists of two prime positive odd integers is proved. Finally, a new concept to study the upper bounds of λ(G) for some special D is introduced. For these sets, the upper bound is improved to 7.

On L(2,1)-labellings of distance graphs

The L(2,1)-labelling number of distance graphs G(D), denoted by λ(D), isstudied. It is shown that distance graphs satisfy λ(G) ≤Δ~2. Moreover, we prove λ({1,2, ..., k})=2k +2 and λ({1,3,..., 2k -1}) =2k + 2 for any fixed positive integer k. Suppose k, a ∈ N and k,a≥2. If k≥a, then λ({a, a + 1,..., a + k - 1}) = 2(a + k-1). Otherwise, λ({a, a + 1, ..., a + k- 1}) ≤min{2(a + k-1), 6k -2}. When D consists of two positive integers,6≤λ(D)≤8. For thespecial distance sets D = {k, k + 1}(any k ∈N), the upper bound of λ(D) is improved to 7.

<i>L</i>(0, 1)-Labelling of Cactus Graphs

An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an L(0,1)-labelling is the maximum label number assigned to any vertex of G. The L(0,1)-labelling number of a graph G, denoted by λ0.1(G) is the least integer k such that G has an L(0,1)-labelling of span k. This labelling has an application to a computer code assignment problem. The task is to assign integer control codes to a network of computer stations with distance restrictions. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label the vertices of a cactus graph by L(0,1)-labelling and have shown that, △-1≤λ0.1(G)≤△ for a cactus graph, where △ is the degree of the graph G.

The L(3,2,1)-labeling on Bipartite Graphs

An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.

<i>L</i>(2,1)-Labeling of the Brick Product Graphs

A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this paper, we show that for or 11, which confirms Conjecture 6.1 stated in [X. Li, V. Mak-Hau, S. Zhou, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, J. Comb. Optim. (2013) 25: 716-736] in the case when or 11. Moreover, we show that? if 1) either (mod 6), m is odd, r = 3, or 2) (mod 3), m is even (mod 2), r = 0.

N-Set Distance-Labelings for Cycle Graphs

Let G = (V, E) be a graph and Cm be the cycle graph with m vertices. In this paper, we continued Yeh’s work [1] on the distance labeling of the cycle graph Cm. An n-set distance labeling of a graph G is the labeling of the vertices (with n labels per vertex) of G under certain constraints depending on the distance between each pair of the vertices in G. Following Yeh’s notation [1], the smallest value for the largest label in an n-set distance labeling of G is denoted by λ1(n)(G). Basic results were presented in [1] for λ1(2)(Cm) for all m and λ1(n)(Cm) for some m where n ≥ 3. However, there were still gaps left unstudied due to case-by-case complexities. For these uncovered cases, we proved a lower bound for λ1(n)(Cm). Then we proposed an algorithm for finding an n-set distance labeling for n ≥ 3 based on our proof of the lower bound. We verified every single case for n = 3 up to n = 500 by this same algorithm, which indicated that the upper bound is the same as the lower bound for n ≤ 500.

针对大规模动态图流三角形计数的边哈希分布式抽样算法

三角形计数是大图分析的一个经典问题,近年的研究工作主要集中在针对静态流式图的三角形数量估计上,相关流式图抽样算法只能处理边的插入操作,无法处理边的删除操作;而现有的动态流式图抽样算法估计准确性又偏低.针对上述问题,提出了基于边哈希分配的分布式抽样(edge hashing assignmentbased distributed sampling,EHADS)算法,它是一个用于估计动态流式图中三角形数量的分布式流算法,可以快速准确地估计动态流式图中的全局三角形数量以及每个顶点的局部三角形数量.EHADS算法只对输入的图流进行1次处理,并在多台机器上对边进行抽样.与先进的单机流算法相比,EHADS算法具有2点优势:1)在相同样本容量的情况下,EHADS算法以更短的运行时间获得了更小的估计误差,估计全局三角形数量的误差平均降低了31.79%,估计局部三角形数量的误差平均降低了23.35%;2)EHADS算法能够提供流式图中三角形数量的无偏估计,并且严格的数学证明显示该无偏估计具有更小的方差.

无蜂窝大规模MIMO系统信道估计中基于加权图的叠加导频分配

针对无蜂窝大规模多输入多输出(cell-free massive multiple-input multiple-output, CF-mMIMO)系统信道估计中导频污染问题,提出了基于加权图的叠加导频(superimposed pilot, SP)分配方案。首先分析导频污染对SP信道估计的影响,引入一种全新度量表示用户间潜在导频污染程度;其次根据接入点与用户间大尺度衰落系数完成用户加权干扰图构建,将系统吞吐量最大化问题转化为有容量最大k切割问题求解;最后采取顶点交换局部搜索算法实现SP次优分配。仿真结果表明:本文方案能够有效地改善SP信道估计误差以及系统吞吐量。

三圈图的(2,2)-可选性的证明

每一个图是(2,2)-可选的猜想迄今未被解决,为了推动(2,2)-可选猜想的证明,利用积和指数的方法证明了所有三圈图是(2,2)-可选的。

Actor-critic框架下的二次指派问题求解方法

二次指派问题(QAP)属于NP-hard组合优化问题,在现实生活中有着广泛应用。目前相对成熟的启发式算法通常以问题为导向来设计定制化算法,缺乏迁移泛化能力。为提供一个统一的QAP求解策略,将QAP问题的流量矩阵及距离矩阵抽象成两个无向完全图并构造相应的关联图,从而将设施和地点的指派任务转化为关联图上的节点选择任务,基于actor-critic框架,提出一种全新的求解算法ACQAP。首先,利用多头注意力机制构造策略网络,处理来自图卷积神经网络的节点表征向量;然后,通过actor-critic算法预测每个节点被作为最优节点输出的概率;最后,依据该概率在可行时间内输出满足目标奖励函数的动作决策序列。该算法摆脱人工设计,且适用于不同规模的输入,更加灵活可靠。实验结果表明,在QAPLIB实例上,本算法在精度媲美传统启发式算法的前提下,迁移泛化能力更强;同时相对于NGM等基于学习的算法,求解的指派费用与最优解之间的偏差最小,且在大部分实例中,偏差均小于20%。

认知无线电网络中基于图着色的动态频谱分配

动态频谱分配是解决认知无线电网络中频谱资源利用率低下的有效手段.针对现有频谱分配中认知用户"饿死"这一难点问题,以最大化系统接入率为目标,提出一种基于图着色的动态频谱分配算法.构造了基于图着色模型的效能函数,通过动态更新可用矩阵完成有效的频谱分配.一系列仿真实验表明,所提算法获得了较高的系统接入率,兼顾了系统的吞吐量和公平性,具有比现有算法更优的性能.

基于图的直方图及路径相似性的图匹配方法

针对图结构在一些非刚性变换下谱特征不稳定等问题,提出一种基于几何关系直方图及路径相似性的图结构信息的描述方法,并在此基础上利用谱分析方法实现图的顶点匹配.首先通过图的直方图给出了一种图顶点的特征描述并初始化候选匹配关系,再基于最短路相似性给出一种匹配关系之间的亲和性的度量,最后采用谱方法求解2个特征点集之间对应关系,实现图的顶点的匹配.与传统的描述方法不同,该方法是利用图的直方图及路径相似性来描述图的结构信息,结构简单,信息描述充分.实验结果表明,文中方法对于一些扰动前后的图的匹配具有较高的匹配准确度.

基于混合蛙跳算法的认知无线电频谱分配

提出一种二进制混合蛙跳算法和基于该算法的认知无线电频谱分配方法。对该方法与颜色敏感图论着色算法进行仿真比较,结果表明在最大化网络总效益和最大化公平效益准则下,基于二进制混合蛙跳算法的频谱分配方法的性能较高。二进制混合蛙跳算法能找到理想最优解,颜色敏感图论着色算法得到的解与理想最优解偏差较大。